Calculate Combination with Replacement in Probability - Definition

Calculate Combination with Replacement in Probability - Formula and Example

Definition:

Combination with replacement in a probability is selecting an object from an unordered list multiple times.

Formula:

CR(n,r) = C(n+r-1,r) = (n+r-1)! / r! (n - 1)! For n >= 0, and r >= 0.
Example:

There are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. You can have three scoops. How many variations will there be?

Given,

n = 5, r = 3

To Find,

Variations with replacement

Solution:

Substitute the values in the formula, CR(n,r) = C(n+r-1,r) = (n+r-1)! / r! (n - 1)! For n >= 0, and r >= 0 Variations = (5+3-1)! / 3!(5-1)! = 7!/3!4! = 5040/6*24 = 35 Hence the value of variation is calculated.

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